Evolution of Alfvén waves by three-wave interactions  in super-Alfvénic shocks

Vainio, R.; Spanier, F.

doi:10.1051/0004-6361:20042433

Cited by 7 publications

(12 citation statements)

References 14 publications

(16 reference statements)

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“…However, the resonant wave-particle interactions could have a damping effect on the turbulence, thus rapidly changing the transmitted wave distributions, especially when moving downstream away from the shock. Similarily, our analysis also neglects the wave-wave interactions in the downstream medium (Vainio & Spanier 2005).…”

Section: Limitations For the Analysismentioning

confidence: 94%

Turbulence transmission in parallel relativistic shocks using ray tracing

Tammi

Vainio

2006

A&A

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We apply a semi-classical approach of handling waves as quasiparticle gas in a slowly varying flow -analogous to ray tracing -to calculate the Alfvén wave transmission parameters, the resulting cross-helicity of the waves and the scattering-centre compression ratio, for cases where the shock thickness is large enough for the turbulent waves in the plasma to see the transition of the background flow parameters as smooth and slowly varying. For nonrelativistic shocks the wave transmission produces similar effects on the downstream turbulence and the scattering-centre compression ratio as does the transmission through a step shock: the downstream Alfvén waves propagate predominantly towards the shock in the local plasma frame and, thus, the scattering-centre compression ratio is larger than the gas compression ratio. For thick relativistic shocks, however, we find qualitative differences with respect to the step-shock case: for low-Alfvénic-Mach-number shocks the downstream waves propagate predominantly away from the shock, and the scattering-centre compression ratio is lower than that of the gas. Thus, when taken into account, the Alfvén wave transmission can decrease the efficiency of the first-order Fermi acceleration in a thick relativistic shock.

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Section: Limitations For the Analysismentioning

confidence: 94%

Turbulence transmission in parallel relativistic shocks using ray tracing

Tammi

Vainio

2006

A&A

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“…The frequencies of the daughter waves as a function of the frequency of the decaying wave in interactions, which fulfill the resonance condition in the whole frequency range including the MHD regime, analysed earlier in 2,5. In the plots Lwaves (blue [dot-dashed] curve), R-waves (green [dashed] curve) and I-waves (red [solid] curve) can be seen.…”

mentioning

confidence: 85%

“…which have been discussed under the MHD approximation already in. 5 They fulfill the resonance condition also in the dispersive limit up to the wave number, where ω T (k) ∼ ω Lo (k), so they are allowed in the low β-regime. We will analyse these reactions numerically below.…”

Section: Low β-Plasmamentioning

confidence: 99%

Three-Wave Interactions of Dispersive Plasma Waves Propagating Parallel to the Magnetic Field

Spanier¹,

Vainio²

2009

adv sci lett

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Three-wave interactions (M ↔ P + Q) of plasma waves propagating parallel to the mean magnetic field at frequencies below the electron cyclotron frequency are considered. We consider Alfvén-ion-cyclotron waves (L), fast-magnetosonic-whistler waves (R), and ion-sound waves (I). Especially the weakly turbulent low-beta plasmas like the solar corona are studied, using the cold-plasma dispersion relation for the transverse waves (L, R) and the fluid-description of the warm plasma for the longitudinal waves (I). We analyse the resonance conditions for the wave frequencies ω and wavenumbers k (i.e., ω M = ω P + ω Q and k M = k P ± k Q , and the interaction rates u MPQ of the waves for all possible combinations of the three wave modes, and list those reactions that are not forbidden. One of the waves has to be longitudinal and two transverse. This demonstrates an attractive feature of the theory: the conservation of angular momentum is implicitly built in. In a low-beta plasma, non-zero reaction rates are obtained for (i) L + ↔ I + + L − and R + ↔ I + + R − in a wide frequency range extending from the MHD frequency range to the resonances of the waves; (ii) for L + ↔ L + + I + in more narrow frequency range, where at least one of the L waves is in the dispersive frequency range; and (iii) I + ↔ L + + R ± close to the resonance of the L mode. The reaction types (ii) and (iii) have, to our knowledge, not been discussed before in low-beta plasmas. In high-beta plasmas, reactions I + ↔ R + + L − and I + ↔ L + + R − are the main reactions, extending down to the MHD frequencies and discussed earlier for the non-dispersive case, but new reactions involving dispersive waves are found in high-beta plasmas as well: I + ↔ L + + R + and R + ↔ I + + R ± are now possible in limited frequency ranges involving at least one dispersive transverse wave. We discuss the implications of the discovered new reactions to turbulent cascading in space plasmas.

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“…Three-wave interaction A three-wave interaction is used to describe the interaction of compressible and incompressible waves in a weakly turbulent plasma and has been described in the first place by Chin and Wentzel (1972). Applications to high-and low-β plasmas are discussed in Vainio and Spanier (2005). For our investigations, where we drive with either pure compressible or pure incompressible fluctuations, one has to put the question with which process compressible fluctuations are generated from incompressible fluctuations and the other way around.…”

Section: Excitation Of Mhd Waves With Compressible or Incompressible mentioning

confidence: 99%

Turbulence evolution in MHD plasmas

Wiśniewski¹,

Kissmann

Spanier³

2013

J. Plasma Phys.

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Turbulence in the interstellar medium has been an active field of research in the last decade. Numerical simulations are the tool of choice in most cases. But while there are a number of simulations on the market some questions have not been answered finally. In this paper we are going to examine the influence of compressible and incompressible driving on the evolution of turbulent spectra in a number of possible interstellar medium scenarios. We conclude that the driving not only has an influence on the ratio of compressible to incompressible component but also on the anisotropy of turbulence.

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Evolution of Alfvén waves by three-wave interactions in super-Alfvénic shocks

Cited by 7 publications

References 14 publications

Turbulence transmission in parallel relativistic shocks using ray tracing

Turbulence transmission in parallel relativistic shocks using ray tracing

Three-Wave Interactions of Dispersive Plasma Waves Propagating Parallel to the Magnetic Field

Turbulence evolution in MHD plasmas

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